Three-way PARAFAC decomposition of chromatographic data for the unequivocal identification and quantification of compounds in a regulatory framework
Introduction
The aim of this work is to show the usefulness of n-way techniques when there are legal requirements to comply with in the performance characteristics of analytical methods, as it is the case of methods for determining residues of veterinary substances, pesticides or some monomers and additives that migrate into food. For these cases, the performance characteristics of the methods are defined in different regulations: Guidance document on analytical quality control and method validation procedures for pesticide residues and analysis in food and feed SANTE/11813/2017 [1] (which updates the contents of SANCO/12495/2011 [2] for pesticides), Decision 2002/657/EC [3] for veterinary drugs residues and EUR 27529 for migration test [4], among others.
There are several chemometric techniques with the second-order advantage that can handle data arrays, so target analytes can be identified and quantified using them even in the presence of interferents that are not included in the calibration standards [5]. In this work, PARAFAC has been considered as a good option. Applications of PARAFAC and PARAFAC2 to chromatographic analysis (in particular, GC-MS and HPLC-DAD) in this regulated context can be found in Refs. [[6], [7], [8]] for pesticides and in the determination of monomers and additives that migrate into food in Ref. [9,10]. In all these cases, the performance of the analyses is regulated.
The usefulness of three-way techniques is also shown with other chromatographic techniques, for example, in the determination of veterinary residues with HPLC-DAD in Ref. [11] or fungicides with LC-MS/MS in Ref. [12]. In addition, Ref. [13] shows the use of these techniques for non-target analyses.
This work develops four case studies with relevant aspects that require to comply with the current legislation, due to the nature of the substances analysed (pesticides and migrants in food, cosmetic additives, etc.). In these cases, the usefulness of n-way techniques (PARAFAC or PARAFAC2) becomes apparent. The results obtained by using the conventional methods are also included to compare them with those obtained with PARAFAC or PARAFAC2.
Although the analytical procedures are focused on two chromatographic techniques (GC-MS and HPLC-DAD), the shown mode of operation is much broader, and can be used with data obtained using a multivariate detector. The most important novelty is the use of the ‘uniqueness property’ to unequivocally identify and quantify the analytes at the same time through the factors of the decompositions.
Uniqueness property is known as the ‘second-order advantage’ [14] in chemical analysis. A trilinear data array is built with the K slabs corresponding to K − h samples of known concentration of a target analyte (calibration standards) together with the h slabs of the test samples. The uniqueness property means that if one of the factors corresponds to the analyte, then the concentration of this analyte can be computed in the test sample even in the presence of interferents that were not in the calibration samples. This property guarantees that there is only one sample profile linked to the analyte of interest, independently of the remaining factors.
Section snippets
Software
MSD ChemStation version E.02.01.1177 (Agilent Technologies, Inc.) with Data Analysis software was used for acquiring and processing data in the case of GC-MS.
OpenLab CDS ChemStation software for an Agilent 1260 Infinity HPLC chromatograph (Santa Clara, CA, USA) was used when the measurements were recorded by means of an HPLC-DAD.
PARAFAC and PARAFAC2 decompositions were carried out with the PLS_Toolbox [15] for MATLAB [16]. Regression models, accuracy lines and kinetic models were fitted and
PARAFAC/PARAFAC2 models
A PARAFAC model of rank F for the array X = (xijk) is written [21, 22] as where are residuals of the fitted model. PARAFAC is a trilinear model, as can be seen in Eq. (1), since it is linear in each of the three profiles.
In general, a three-way data array X (I × J × K) is made up of real numbers, xijk, i = 1, …, I; j = 1, …, J; k = 1, …, K. In the case of GC-MS data, each value xijk would be the abundance recorded at the
Case I: Interferents with overlapping peaks to the internal standard and the target analyte (BPA)
The internal standard used in the determination of bisphenol A (BPA) by GC-MS was its deuterated compound, BPA-d16, so both compounds closely elute. When analysing samples from the migration test of BPA from polycarbonate tableware, several interferents coeluted. Fig. 2 shows the total ion chromatogram obtained in full scan mode (500 μg L−1 of each analyte in the extract obtained from the simulant (ethanol:water)). The experimental details of the multiresidue analysis of BPA, bisphenol F
Conclusions
The use of PARAFAC/PARAFAC2 models enables the unequivocal identification of the target compounds according to the regulation in force in each case analysed.
The internal standard used in the determination of bisphenol A (BPA) by GC-MS was its deuterated compound, BPA-d16, so both compounds closely elute. When analysing samples from the migration test of BPA from polycarbonate tableware, several interferents coeluted preventing the identification of BPA. The relative abundances of the detected
CRediT authorship contribution statement
M.C. Ortiz: Conceptualization, Methodology, Writing - original draft, Supervision, Writing - review & editing, Funding acquisition. S. Sanllorente: Investigation, Methodology, Supervision. A. Herrero: Investigation, Methodology, Supervision. C. Reguera: Investigation, Methodology, Supervision. L. Rubio: Investigation, Methodology, Writing - original draft, Supervision, Writing - review & editing. M.L. Oca: Investigation, Methodology. L. Valverde-Som: Investigation, Methodology, Supervision,
Declaration of competing interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgements
The authors thank the financial support provided by Spanish Ministerio de Ciencia Innovación y Universidades (AEI/FEDER, UE) through project CTQ2017-88894-R and by Consejería de Educación de la Junta de Castilla y León through project BU012P17 (all co-financed with European FEDER funds). M.M. Arce wish to thank Junta de Castilla y León and Fondo Social Europeo for her predoctoral grant.
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2022, Microchemical JournalCitation Excerpt :The most common ones are generalized rank annihilation method (GRAM), multivariate curve resolution by alternating least squares (MCR-ALS), parallel factor analysis (PARAFAC/PARAFAC2), direct trilinear decomposition (DTLD), TUCKER3, and N-way partial least squares and unfolded partial least squares which later require residual trilinearization (N-PLS/RTL and U-PLS/RTL) [7–9]. Among them, some authors prefer PARAFAC as a chemometric tool for their analyses of pharmaceuticals [8] and of food matrices [10,11] due to the easier interpretation of the results obtained from higher order datasets, to the simple and fast quantitative estimation, and to the better values of performance criteria. Therefore, the possibility of applying the advantages that PARAFAC provided as a decomposition technique could be considered for this work.